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Chapter 7. Game of Life

One of the first cellular automata to be studied (and probably the
most popular of all time) is a 2D CA called “The Game of Life,” or GoL for
short. It was developed by John H. Conway and popularized in 1970 in
Martin Gardner’s column in Scientific American. See
http://en.wikipedia.org/wiki/Conway_Game_of_Life for
more information.

The cells in GoL are arranged in a 2D grid, either infinite in both directions or wrapped
around. A grid wrapped in both directions is called a torus because it is topographically equivalent to
the surface of a doughnut; see http://en.wikipedia.org/wiki/Torus.

Each cell has two states (live and dead) and eight neighbors (north,
south, east, west, and the four
diagonals). This set of neighbors is sometimes called a Moore neighborhood.

The rules of GoL are totalistic,
which means that the next state of a cell depends on the number of live
neighbors only, not on their arrangement. The following table summarizes
the rules:

Number of
neighbors

Current state

Next state

2–3

live

live

0–1,4–8

live

dead

3

dead

live

0–2,4–8

dead

dead

This behavior is loosely analogous to real cell growth: cells that
are isolated or overcrowded die, but at moderate densities they
flourish.

GoL is popular for the following reasons:

There are simple initial conditions that yield surprisingly
complex behavior.

There are many interesting stable patterns: some oscillate (with
various periods), and some move like the spaceships in Wolfram’s Rule
110 CA.

Like Rule 110, GoL is Turing complete. ...

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